Set 17: Exponential Functions (Advanced)

Choice A is correct. Choice A is the correct answer. Find $a$ and $b$. 1. Find a: Y-intercept is $(0, 3)$, so $a=3$. 2. Substitute: Use $(2, 12)$ in $y = 3 b^x$. $12= 3 b^2$. 3. Solve: $b^2 = 4 \implies b = 2$ (since base must be positive). 4. Equation: $y = 3(2)^x$. Strategic Tip: If given $x=2$, you need to take the square root to find $b$. Choice B is incorrect because $3(4)^2 = 3(16) = 48 \neq 12$. Choice C is incorrect because it starts at 12. Choice D is incorrect because it is linear.